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On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization andMixed Reformulation

Published online by Cambridge University Press:  27 January 2009

F. Ben Belgacem ,
C. Bernardi ,
A. Blouza  and
M. Vohralík
F. Ben Belgacem
Affiliation:
L.M.A.C. (E.A. 2222), Département de Génie Informatique, Université de Technologie de Compiègne, Centre de Recherches de Royallieu, B.P. 20529, 60205 Compiègne Cedex, France
C. Bernardi*
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
A. Blouza
Affiliation:
Laboratoire de Mathématiques Raphaël Salem (U.M.R. 6085 C.N.R.S.), Université de Rouen, avenue de l'Université, B.P. 12, 76801 Saint-Étienne-du-Rouvray, France
M. Vohralík
Affiliation:
Laboratoire Jacques-Louis Lions, C.N.R.S. & Université Pierre et Marie Curie, B.C. 187, 4 place Jussieu, 75252 Paris Cedex 05, France
*
bernardi@ann.jussieu.fr
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Abstract

The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem and establish optimal a priori error estimates.

Keywords

unilateral contactelastic membranesvariational inequalities
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 4 , Issue 1: Modelling and numerical methods in contact mechanics , 2009 , pp. 21 - 43
Copyright
© EDP Sciences, 2009

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